{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Chapter 4, demo 1\n",
    "\n",
    "Bayesian Data Analysis, 3rd ed\n",
    "\n",
    "Normal approximation for Bioassay model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import preliz as pz\n",
    "from scipy.optimize import minimize\n",
    "pz.style.use('preliz-doc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Bioassay data, (BDA3 page 86)\n",
    "x = np.array([-0.86, -0.30, -0.05, 0.73])\n",
    "n = np.array([5, 5, 5, 5])\n",
    "y = np.array([0, 1, 3, 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the posterior density in grid\n",
    " * usually should be computed in logarithms!\n",
    " * with alternative prior, check that range and spacing of A and B are sensible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ngrid = 100\n",
    "A = np.linspace(-4, 8, ngrid)\n",
    "B = np.linspace(-10, 40, ngrid)\n",
    "ilogit_abx = 1 / (np.exp(-(A[:,None] + B[:,None,None] * x)) + 1)\n",
    "p = np.prod(ilogit_abx**y * (1 - ilogit_abx)**(n - y), axis=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following demonstrates an alternative \"bad\" way of calcuting the posterior density p in a for loop. The vectorised statement above is numerically more efficient. In this small example however, it would not matter that much.\n",
    "\n",
    "    p = np.empty((len(B),len(A))) # allocate space\n",
    "    for i in range(len(A)):\n",
    "        for j in range(len(B)):\n",
    "            ilogit_abx_ij = (1 / (np.exp(-(A[i] + B[j] * x)) + 1))\n",
    "            p[j,i] = np.prod(ilogit_abx_ij**y * ilogit_abx_ij**(n - y))\n",
    "\n",
    "N.B. the vectorised expression can be made even more efficient, e.g. by optimising memory usage with in-place statements, but it would result in a less readable code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# sample from the grid\n",
    "nsamp = 1000\n",
    "samp_indices = np.unravel_index(\n",
    "    np.random.choice(p.size, size=nsamp, p=p.ravel()/np.sum(p)),\n",
    "    p.shape\n",
    ")\n",
    "samp_A = A[samp_indices[1]]\n",
    "samp_B = B[samp_indices[0]]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "samp_A += (np.random.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "samp_B += (np.random.rand(nsamp) - 0.5) * (B[1]-B[0])\n",
    "\n",
    "# samples of LD50\n",
    "samp_ld50 = - samp_A / samp_B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the mode by minimising negative log posterior. Compute gradients and Hessian analytically, and use Newton's method for optimisation. You may use optimisation routines below for checking your results. See help for scipy.optimize.minimize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define the optimised function\n",
    "def bioassayfun(w):\n",
    "    a = w[0]\n",
    "    b = w[1]\n",
    "    et = np.exp(a + b * x)\n",
    "    z = et / (1 + et)\n",
    "    e = - np.sum(y * np.log(z) + (n - y) * np.log(1 - z))\n",
    "    return e\n",
    "# initial guess\n",
    "w0 = np.array([0.0, 0.0])\n",
    "# optimise\n",
    "optim_res = minimize(bioassayfun, w0)\n",
    "# extract desired results\n",
    "w = optim_res['x']\n",
    "S = optim_res['hess_inv']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the normal approximation density in grid this is just for the illustration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create a grid of (A, B) points\n",
    "AA, BB = np.meshgrid(A, B, indexing='ij')  # shape (ngrid, ngrid)\n",
    "# Stack into (ngrid, ngrid, 2) for multivariate pdf\n",
    "grid = np.stack((AA, BB), axis=-1)\n",
    "# Evaluate multivariate normal pdf\n",
    "p_norm = pz.MvNormal(mu=w, cov=S).pdf(grid)\n",
    "# draw samples from the distribution\n",
    "samp_norm = pz.MvNormal(mu=w, cov=S).rvs(size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 900x1000 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 2, figsize=(9, 10))\n",
    "\n",
    "# Define common axis limits\n",
    "xlim, ylim = [-2, 6], [-10, 30]\n",
    "ld50_bins = np.linspace(-0.8, 0.8, 31)\n",
    "ld50_xticks = np.linspace(-0.8, 0.8, 5)\n",
    "\n",
    "bpi = samp_norm[:,1] > 0\n",
    "samp_ld50_norm = -samp_norm[bpi,0] / samp_norm[bpi,1]\n",
    "\n",
    "# Posterior densities\n",
    "for ax, p_ in zip(axes[0], [p, p_norm]):\n",
    "    ax.imshow(p_, origin='lower', aspect='auto', extent=(A[0], A[-1], B[0], B[-1]))\n",
    "    ax.set(xlim=xlim, ylim=ylim, xlabel=r'$\\alpha$', ylabel=r'$\\beta$')\n",
    "    ax.grid(False)\n",
    "\n",
    "# Posterior samples\n",
    "for ax, sample in zip(axes[1], \n",
    "                      [(samp_A, samp_B), (samp_norm[:,0], samp_norm[:,1])]):\n",
    "    ax.scatter(*sample, s=5)\n",
    "    ax.set(xlim=xlim, ylim=ylim, xlabel=r'$\\alpha$', ylabel=r'$\\beta$')\n",
    "    ax.text(0, -7, f'p(beta>0)={np.mean(sample[1]>0):.2f}')\n",
    "\n",
    "# LD50 histograms\n",
    "for ax, ld50 in zip(axes[2], [samp_ld50, samp_ld50_norm]):\n",
    "    ax.hist(ld50, bins=ld50_bins)\n",
    "    ax.set(xlim=[ld50_bins[0], ld50_bins[-1]], xlabel=r'LD50 = -$\\alpha/\\beta$', yticks=(), xticks=ld50_xticks)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bda_py_demos",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
